Photodetectors with excellent time resolution are becoming increasingly important in many applications in medicine, high energy- and nuclear physics applications, biology, and material science. Silicon photomultipliers (SiPM) are a novel class of solid-state photodetectors with good timing properties. While the time resolution of analog SiPMs has been analyzed by many groups, the time resolution of the digital photon counter (DPC) developed by Philips has not yet been fully characterised. Here, the timing capabilities of the DPC are studied using a femtosecond laser. The time resolution is determined for complete dies, single pixels, and individual single photon avalanche diodes (SPADs). The measurements cover a broad dynamic range, from intense illumination down to the single-photon level, and were performed at various temperatures between 0°C and 20°C. The measured single photon time resolution (SPTR) ranges from 101 ps FWHM for the DPC3200 sensor pixel to 247 ps FWHM for the DPC6400 sensor die. An extensive study of the single-SPAD time resolution, ranging from single photon to very high laser intensities (∼1000 photons per pulse), yielded a time resolution of 48 ps FWHM at the single-photon level.